Which of these numbers is prime? ${15,\ 33,\ 40,\ 67,\ 77}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 15 are 1, 3, 5, and 15. The factors of 33 are 1, 3, 11, and 33. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The factors of 67 are 1 and 67. The factors of 77 are 1, 7, 11, and 77. Thus, 67 is a prime number.